- 09-57 Helge Krueger and Gerald Teschl
- Unique continuation for discrete nonlinear wave equations
Mar 31, 09
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Abstract. We establish unique continuation for various discrete nonlinear wave equations.
For example, we show that if two solutions of the Toda lattice coincide for one lattice point in some
arbitrarily small time interval, then they coincide everywhere. Moreover, we establish analogous results
for the Toda, Kac-van Moerbeke, and Ablowitz-Ladik hierarchies. Although all these equations
are integrable, the proof does not use integrability and can be adapted to other equations as well.